Skip to main content
SpringerLink
Log in

Solution for free vibration problem of membrane with unequal tension in two directions

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, we obtain the analytic solution of free vibration frequency and mode shapes of rectangle, circle and elliptic membranes. The approximate solution of membrane with arbitrary boundary is also obtained. All of these membranes are acted on by unequal tension in two directions.

For the rectangle membrane, in this paper we transform its vibration equation into one of usual membranes by transforming the coordinate, thus it is easy to get the solution. For the way we deal with the rectangle membrane. Next we transform the vibration equation into the Mathieu equation, then we get a formula of frequency of that membrane with some Mathieu function's property. In the solution the elliptic membrane is similar to that of the circle membrane.

Finally, some examples are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Solar, A. I. and H. Afshard,On the Analysis of Cable Network Vibration Using Calerkin Method, J. Appl. Mech. Proc. ASME. Vol. 37, No. 3, Sept. (1970), 606–611.

  2. Leonard, John W.,Incremental Response of 3-D Cable Networks, J. Eng. Mech. Div. ASCE., 99, No. EM 3, Proc. Paper 9765, June (1973), 621–629.

    Google Scholar 

  3. Murari, L. Gambhir and Barriangton de V. Batchelor,Free Vibration of Taut Cable and Plane Cable Nets, J. Struct. Div. ASCE, 103 No. STLL. Nov., (1977), 2264–2268.

    Google Scholar 

  4. Gambhir, M. L. and Barrington de V. Batchelor,A Finite Element for 3-D Prestressed Cablenets, Inter. J. Nume. Eng., 11. No. 11 (1977), 1699–1718.

    Google Scholar 

  5. Leonard, J.W.,Nonlinear Dynamics of Curved Elements, J. Eng. Mech. Div., ASCE, Vol. 99, (1973), 616–621.

    Google Scholar 

  6. Mclachlan, N. W.,Theory and Application of Mathieu Functions, Oxford at the Clarendon Press, (1947).

  7. Jin Wen-lu,Calculation of Suspended Structures, Chinese Building Industry Press, (1975). (in Chinese)

Download references

Author information

Authors and Affiliations

  1. Hangzhou Design Institute of Architecture, Hangzhou, China

    Qian Guo-zhen

Authors
  1. Qian Guo-zhen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Chien Wei-zang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo-zhen, Q. Solution for free vibration problem of membrane with unequal tension in two directions. Appl Math Mech 3, 885–892 (1982). https://doi.org/10.1007/BF01895343

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01895343

Keywords

Search

Navigation